Question: Find all solutions to the equation $\displaystyle\sqrt[3]{3 - x} = -\frac{3}{2}$.
Solution: We get rid of the cube root sign by cubing both sides.  This gives us $3-x = -\frac{27}{8}$.  Solving this equation gives $x = 3 + \frac{27}{8} = \boxed{\frac{51}{8}}$.